Use Case Title: Soft Shopping Agent

Purpose/Goals (Summarize what the use case is to accomplish)Suppose we have a car selling web site offering cars and we would like to buy a car. Descriptions of the cars are stored in databases and we have some ontology encoding information about the domain. Now, suppose that preferably we would like to pay around 11000 euro and the car should have fewer than 15000 km on the odometer. Also, if there are leather seats then I would like to have air conditioning, the color is preferably blue, and the car is is not old.

Of course, most of our constraints, e.g. on price and kilometers, aren't crisp as we may still accept e.g.~a car's cost of 11200 euro and with an odometer reading of 16000km. Hence, these constraints are rather vague (fuzzy) (we may model this by means of so-called fuzzy memebr functions). We may also give some preference weight to my requirements.

On the other hand, the seller may offer a discount on the car's catalogue price, but the bigger the discout the less satisfied he is. For instance, related to the e.g a sold Mazda3, the seller may consider optimal to sell above 15000euro, but can go down to $13500euro to a lesser degree of satisfaction.

For each car, there will be an optimal price it can be sold, which maximises the product of the buyer's degree of satisfaction and the seller's degree of satisfaction. This is the so-called NASH equilibrium of the matching. Each car gets an optimal degree of buyer/seller degree of satisfaction.

From the buyer perspective, he asks for the TOP-k cars and their optimal price, ranked the optimal degree of sadisfaction.

From the seller perspective, he may ask for the TOP-k buyer's for a given car and their optimal price, ranked the optimal degree of sadisfaction.

Issues and Relevance to Uncertainty (Summarize how relevant to uncertainty reasoning and representation?)

Matchmaking in eCommerce with soft constraints is about vague reasoning. The uncertainty type is vagueness(UncertaintyType:Vagueness), as matchings are found only to some degree. The possible model is based on mathematical fuzzy logic(UncertaintyModel:Fuzzy Sets). An optimization and reasoning procedure is involved (Agent:Machine:Machine Deduction - optimizing finding top-k answers on the web).

Assumptions/Preconditions (List the preconditions necessary for this use case to occur, including description of necessary context)